The Bronx, which has the highest percentage of poor households, sends the fewest, a fact that has prompted Borough President Ruben Diaz Jr. to propose an overhaul of the schools' admissions policy.

Mr. Diaz said he believed that basing admissions solely on the results of one test taken by thousands of eighth graders each year had excluded too many Bronx children who are academically gifted, but whose families cannot afford the private test preparation classes that wealthier families pay for.

In a report Mr. Diaz is releasing on Wednesday, he recommends that children performing in the top 5 percent of each Bronx middle school be automatically permitted to enroll in one of the eight specialized high schools, and that the city open more of these elite high schools in his borough.

"We have some of the brightest middle school students in the City, if not the nation, right here in the Bronx," Mr. Diaz said in a statement. "It is time for the Department of Education to provide the Bronx with the proper resources to make sure that their minds can thrive."

City officials said they had no plans to move away from a test-based admissions policy.

Of the roughly 4,700 Bronx eighth graders who took the specialized high school admissions test this year, 322 scored high enough to be admitted, a 7 percent success rate. In Manhattan, 32 percent of the students who took the test received an offer to one of the elite schools.

At Stuyvesant High School, an elite school in Manhattan, Hispanic students make up 2.4 percent of the enrollment, compared to 40.3 percent of the city's entire school system. Black students account for 32 percent of the city's public school students, but are 1.2 percent of the population at Stuyvesant.

Many of the students who are admitted spent months, if not years, in private test prep classes, some of which are run by tutoring behemoths like Kaplan, but others are homegrown companies that have popped up, particularly in Queens neighborhoods, where the demand for low-cost tutoring is often on display in shopping malls and storefronts.

These cheaper options are in short supply in the Bronx, and few residents can afford the more expensive options, so many students rely on the city's free test prep institute, which was created to improve the performance of members of underrepresented minorities.

But the borough president's report is highly critical of the institute, which the city renamed Dream this year, and expanded its enrollment to include an additional 500 students. The program is open to sixth and seventh graders who have high scores on the state math and English exams, at least a 90 percent middle school attendance rate, and whose parents' income qualifies them for free or reduced lunch.

"We share the excitement and the hopes of thousands of students who will participate in this year's Dream institute, and we fully support the rigorous standard to attend our most selective schools," said Matt Mittenthal, a spokesman for the city's Education Department.

Raymond Sanchez, the director of policy for Mr. Diaz, said the institute should set aside more seats for Bronx students and end its 90 percent attendance requirement. Too many Bronx students have extended absences for medical reasons, or for family trips to their native countries, he said.

"These kids aren't even close to 90 percent," he said. "If you have a kid who can do the work, what does it matter what their attendance rate is?"

Bronx students' scores on the state math and English exams are also quite low. Last year, about 31 percent of them scored high enough to be considered proficient in English, compared to 51 percent in Queens.

The borough president's report also calls for more gifted classes for younger students, who typically test into the program as 5-year-olds.

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